Numerical curve generator in a machine tool system

ABSTRACT

A method and system for determining the advance of a curve to be created on an X-Y plane, wherein the distances X and Y between the current position of the curve and a specific point assumed in correspondence with the nature of the curve and along the x-axis and the y-axis of the plane are utilized. The large-small relationship of the pulse distribution densities to the axes is decided from the large-small relationship of X and Y. As a result of this decision, the axis of higher pulse distribution density is distributed with pulses and a decision is made whether or not to simultaneously apply pulses to the other axis according to the qualitative value (positive, negative, or zero) of the current operational result as determined by the relationships: Delta &#39;&#39; (PRECEDING OPERATIONAL RESULT Delta &#39;&#39;) + (DIFFERENCE BETWEEN X and Y) or (PRECEDING OPERATIONAL RESULT Delta &#39;&#39;) - (THE SMALLER OF X and Y). At the same time, by fixing the specific point or by moving it in correspondence to the advancing curve, functions corresponding to straight lines, arcs, parabolas, hyperbolics, ellipses, spirals, group circles, exponential curves, logarithmic curves, and other figures can be generated in a simple manner.

ite States Patent 11 1 1111 3,763,363

Saita et al. 1 Oct. 2, 1973 NUMERICAL CURVE GENERATOR IN A Primary ExaminerFelix D. Gruber MACHINE TOOL SYSTEM Assistant ExaminerDavid H. Malzahn Att0rneyWard, McElhannon, Brooks & Fitzpatrick [75] Inventors: Nobuo Salts; Yo chl Tanaka, both of and Joseph M. Fitzpatrick et a1 Int Ina, Japan [73] Assignee: gabulfhilltli Klazisha YltlasklwajDenki [57] ABSTRACT elsa us l ayus u s apan A method and system for determining the advance of [22] Filed: Mar- 23, 19 1 a curve to be created on an X-Y plane, wherein the dis- [211 pp No, 127 289 tances X and Y between the current position of the curve and a specific point assumed in correspondence with the nature of the curve and along the x-axis and Foreign pp Priority Data the y-axis of the plane are utilized. The large-small rela- Mar. 24, 1970 Japan 45 25093 tionship of he pulse distribution densities to the axes M 27 1970 Japan 45/26190 is decided from the large-small relationship of X and Y.

A 9 1970 JapanM 45/30967 As a result of this decision, the axis of higher pulse dis- Sept. 19, 1970 Japan 45 112403 tribution den i y i di ributed with pulses and a deci- 1 sion is made whether or not to simultaneously apply [52] 11.8. CI. 235/152, 235/l51.1l pul es to he other axis according to the qualitative [51] Int. Cl. (206i 15/46 value (p negative, or zero) of the rr n p ra- [58] Field of Search 235/152, 151.11 tion l r l as determined by the relationships:

A (preceding operational result A) (difference [56] References Cited between X and Y) UNITED STATES PATENTS of 3,254,203 5/1966 Kreim 235/152 (Preceding peratinal (the Smaller 3,591,780 6/1971 Rosenfeld 235/152 x of X and 3,555,253 1/1971 Seki 235/151.11 At the same time, by fixing the specific point or by 3,564,595 2/1971 De Florio et al. 235/152 X moving it in correspondence to the advancing curve,

OTHER PUBLICATIONS functions corresponding to straight lines, arcs, parabolas, hyperbolics, ellipses, spirals, group circles, exponential curves, logarithmic curves, and other figures can be generated in a simple manner.

W. C. Cook, Digital Line-Circle Generator IBM Technical Disclosure Bulletin Vol. 12 No. 10 Mar. 1970 p. 1605 5 Claims, 75 Drawing Figures COMMAND(X,Y) A' 0 103 101 REGISTER 104 1 (PER CYCLE dy=l WHENASO (X) d =0"wHENA o 102 REGISTER 101 REGISTER I F T06 ADDER COMPLEMENT PATENTEU 21975 3.763.363

saw (:1 nr 17 7 FIG. l 00 0 0 0X x AXIS 1 0 bl b2 by y AX|S t F l G. 2

x AXIS y AXIS y AXIS X Y I STANDARD PATENTED 2|975 3.763.363

sum 02 or 17 FIG.7

COMMAND (X,Y)

lOl REGISTER (PER' CYCLE "w EN A o dX: dyo- WHEN A 0 REGISTER I02 REGISTER I05 COMPLEMENT Fl G a START W, c IPERCYCLEI I T nnm 2197a 3, 753,353

sum 03 or w m FI I2 dx=l' WHEN dx="|' (PER Q wm w Ago .I I dy: I, dxzo WHEN A O WHEN d gf I02 REGISTER (PER CYCLE dx= I (PER CYCLE) WHEN Ago dy=I, CIX='O' WHEN A 0 IT REGISTER I02 REGISTER I06 ADDER PATENTED 21973 3,763,363

SHEET ouor I7 AO d I x=I REG'STER (PER CYCLE) WH N Ago WI-EN dx=| d dx-O (X) WHEN A O y IIOZLREGISTER I REGISTER WHEN =I' Y I A (PER CYCLE) Tl l 5 coIPPLEMENT I s ADDER FIG. I9

y I9I x x-I x-z Fl '20 (b) x X-l x-2 X AXIS M 7 0 f y 0-0 1' F B 2! m TIMES PER n CYCLES IoI REGISTER I04 dxf WHEN dx=I dy=*|, wHE N Aio -l dx=O I02 REGISTER I07 QQ (PER CYCLE) c COMPLEMENT ADDER PATENTED 3,763,363

' sum 05 If 1T I02 REGISTER REGISTER C I05 COMPLEMENT FIG. 24

F l G. 25

FIG.26

FIG. 27

I6. 32 y P(x,Y)

i EY O X Q X PATENTED [1U 21973 sum DD M 1% PIC yL mx) LINEAR COMMAND 390 O XL F l G. 29 y ARCuATE 40o COMMAND 1 [I l- F' I G. 30 MW LINEAR COMMAND i XL [STEP I] yc ARCUATE COMMAND i I Q;

M X L. r! C F l G. 54

x Li L T 1 k I I I y AXIS 340lg34O2;303,+ 3404: m 3405 i 3406 '0 '9 0 a DIRECTION OFADVANCE 'o O O 45 45 0 UOFTRACKINGT PATENTEDBET 2 3,763,363

swan as w [STEP 1) STOPAT T O FIG.46 H647 yL yo LINEA COMMAND ARCUATE COMMAND ,M X L [STEP 2] PATENTEUUBT 2 I915 3,763,863

ARCUATE OPERATION ONE CYCLE RC! 1 LINEAR A ATE A COMMAND COW 0 (Tr.0) X0 0 XL PATENTEU OUT 2 75 LINEAR OPERATION ON CYCLE ARCUATE OPERATION ONE CYCLE STOP AT Tr O PfiJi'EFHE-Q B 2W5 3.763.363

sum :11 or w FIG.55

SERIES xAXiS H TOLERANCE yAXIS DIRECTIONOFX AXIS POSITIVE NEGATIVE ADVANCE y AXIS |NEGATIVE POSITIVE (POSITIVE FIG.6O

FIG.57

OPERATION 59 3 COMMAND 0 mfimw 2 3,763,363

saw m [If 17 Fl 6. 64 Fl 6. 65

ROTATION TYPE TRANSLATION TYPE y y OBJECTIVE FIG.7|

PATENTEDUET 21913 3.763.363

sum 1a or 17 FIG.7O

NUMERICAL CURVE GENERATOR IN A MACHINE TOOL SYSTEM BACKGROUND OF THE INVENTION BRIEF DESCRIPTION OF THE DRAWINGS This invention relates to digital function generation explanation of the fundamental principle of this invenparticularly for numerical control of work processes.

While a number of methods such as the so-called MIT (extraction of non-carrier pulses of a counter) method, DDA (extraction of overflow pulses of a digital integrator) method, and the algebraic computation (computation of algebraic discrimination type) method have heretofore been known for digital function generation, there has been none which occupies a position of absolute dominance for numerical control. That is, control of pulse distribution velocity, correction of the functions corresponding to a cutting tool, and, of course, smoothness of the interpolation effect are required in numerical control, and the total hardward necessitating computation of segment lengths and radii with respect to these requirements is caused to be complicated.

This invention is a creative result of technical thinking which is a complete departure from established concepts and affords the advantageous features of: (l) elimination of effects on the pulse distribution velocity due to the kind and magntiude of the function; (2) interpolation effect of curves due to pulses which is smoother than that of any known technique; (3) marked simplification of the hardware; and (4) the possiblity of freely generating, by gate operations, functions of straight lines, arcs, parabolas, hyperbolas, ellipses, spiral curves, group circles, logarithmic curves, exponential curves, and other curves.

SUMMARY OF THE INVENTION According to the present invention, briefly summarized, there is provided a method wherein, as a result of intensive investigation into the basic characteristics v of curves in a plane, a specific center is determined for tracking of a curve by digital pulse distribution, this center point being fixed or caused to move, and a large number and variety of functions are generated in accordance with rotations about this center point or translational movement.

The basic principle of the pulse distribution according to the invention resides, in the progressive generation of a curve in a plane of x, y coodinate axes by pulse distribution in the direction of both axes, in the continual taking of the axis of higher pulse distribution density as a standard and effecting a decision as to whether 1 or not to distribute pulses in the direction of the axis of lower pulse distribution density.

By the practice of this invention, the hardware therefor becomes concise and economical, and the software is simplfied. Furthermore, the resulting error in curve tracking is within one quantized unit whereby it is possible to generate functions of higher precision than those of various apparatus involving digital function generators heretofore known in the art.

The nature, principle, and utility of this invention will be more. clearly apparent from the following detailed description with respect to preferred embodiments of the invention when read in conjunction with the accompanying drawings, in whichlike parts are designated by like referencenumerals and characters.

tion;

FIGS. 4, 5, 6(a) and (6b) are graphical representations and FIGS. 7 and 8 are block diagrams for a description of the determination of pulse distribution for 0 linear tracking and the hardware and software therefor;

FIGS. 9, 10, and 11 are graphical representations and FIG. 12 is a block diagram for a description of the determination of pulse distribution for arcuate tracking and the hardware therefore;

FIGS. 13 and 14 are graphical representations and FIG. 15 is a block diagram for a description of the determination of pulse distribution for parabolic tracking and the hardware therefor;

FIGS. 16 and 17 are graphical representations and FIG. 18 is a block diagram for a description of the determination of pulse distribution for hyperbolic tracking and hardward therefor;

FIGS. 19 20(a) and 20(b) are graphical representations and FIG. 21 is a block diagram for a description of the determination of pulse distribution for elliptical tracking and the hardware therefor;

FIGS. 22 and 23 are respectively a graphical representation and block diagram indicating the manner in which a command value appraoching the true value is imparted by the function generation according to this invention;

FIGS. 24 through 27, inclusive, are graphical representations for a comparison between the digital function generating system of this invention and three other like systems with respect to linear tracking;

FIGS. 28, 29 and 30 are graphical representations for a comparison between the digital function generating system of this invention and two other like systems with respect to arcuate tracking;

FIGS. 31, 32, 33, and 34 are graphical representations indicating a procedure for causing the velocity in pulse distribution to be constant in this invention;

FIG. 35 is a graphical representation and FIGS. 36 and 37 are block diagrams indicating an example of practice of pulse distribution for obtaining this constant velocity;

FIG. 38 is a diagram, FIGS. 39 and 40 are graphical representations, and FIG. 41 is a block diagram for a description of the path of travel of a tool (a cutter) when it cuts a workpiece in a straight line through an application of this invention and the software therefor;

FIG. 42 is a diagram, FIGS. 43, 44, 46, and 47 are graphical representations, and FIGS. and 48 are block diagrams for a description of the path of travel of a tool (a cutter) when it cuts a workpiece along an are through an application of this invention and the software therefor;

FIG. 49 is a diagram, FIGS. 50-and 51 are graphical representations, and FIG. 52 is a block diagram for a description of the path of travel of a tool (a cutter) when it cuts a workpiece having a point of inflection through an application of this invention and the software therefore;

FIG. 53 is a diagram indicating the cutting of a hole of a desired diameter with a single tool (a cutter) which undergoes a spiral motion transitting into a circular motion;

FIG. 54 is a diagram, partly in perspective, indicating the cutting a workpiece by means of a cutting tool undergoing a motion of group circles;

FIG. 55 is a table, FIGS. 56, 57, and 60 are graphical representations, and FIGS. 58 and 59 are block diagrams for a description of the pulse distribution for generation of functions of spiral configuration according to this invention and of the hardware and software therefor;

FIGS. 61 and 62 are graphical representations and FIG. 63 is a diagram indicating a pulse distribution method for generation of group circle functions according to the invention and the application thereof to cutting a workpiece of conical shape;

FIG. 64 is a diagram for a description of a curve of rotation type as herein referred to for tracking a curve as it rotates about a point P;

FIG. 65 is a diagram for a description of a curve of translation type" as herein referred to for tracking a curve as it advances in a straight line with respect to an objective P;

FIG. 66 and 67 are block diagrams indicating the hardware and software for tracking a curve of the above mentioned translation type;

FIG. 68 is a graphical representation indicating a mathematical analysis of an exponential curve resulting from the above mentioned technique of translation p FIG. 69 is a table indicating variations in generated functions accompanying variations in the tolerances AA and AB of the x and y axes in the above mentioned translation-type technique;

FIG. 70 is a table indicating in relatively greater detail the moving fixes (from P through Pn) and the antipodal points of the generated curves of FIG. 69;

FIG. 71 is a table showing variations in the generated functions accompanying variations is the tolerances AA and AB of the x and y axes in the above mentioned rotation type" technique;

FIG. 72 is a table indicating in relatively greater detail the moving fixes (from P0 through Pn) and antipodal points of the generated curve of FIG. 71; and

FIG. 73 is a drawing of reduced scale showing curves drawn as a result of actual function generation by means of a system according to this invention.

DETAILED DESCRIPTION OF THE INVENTION When a two-dimensional function F(x,y) 0 is considered, it is apparent that while it isnecessary to maintain a specific relationship between the independent variables x and y thereof, the relationship between x and y can be divided by introducing thereinto a third parameter t into two functions, namely, (t and x) and (t and y).

A feature of this invention is that by representing these two divided functions by respective independent arithemetic progressions or series and specifying the first term thereof and'tolerance, any of various curves such as straight lines, arcs, parabolas, hyperbolas, ellipses, spiral curves, and group circles are digitally generated within an error range of one quantized unit. Furthermore, certain curves such as logarithmic curves and exponential curves which cannot be represented by arithmetic series can also be generated by the same technique, The manner in which these functions are generated in accordance with the invention will become apparent as the following detailed description progresses.

FIG. 1 graphically illustrates a series a a a, having a first term 0 and representing the relationship between the independent variable x and the parameter t and a series b, b,, b having a first term b, and representing the relationship between the independent variable y and the parameter r. In this figure, the symbols@ each consisting of a circle with a vertical diametric line, indicate the pulse distribution, and each of the terms in the two series corresponds to a respective one of the pulses.

By taking the variation of the independent variables x and y corresponding to the distribution of one pulse as one quantized unit, the following equations of relationships are obtained.

where i-= 0,1, 2,

wherej=0, l, 2,.

When plotted with respect to x,t and y,! axes, Eq. 1 and Eq. 2 appear as indicated in FIG. 2 by discontinuous or zigzag lines 22 and 23, respectively, the envelopes of which are intermittent lines 20 and 21. The relationship between the independent series x and y which results when the parameter r is eliminated from FIG. 2 is indicated in FIG. 3. That is, since t is a common parameter in Eq. 1 and Eq. 2, the first function F (x,y) 0 is generated digitally by causing the terms of the two series to progress as the sums of the two series are maintained equal. In addition, the principle of function generation is indicated wherein the relationship bg; t lie 1 (Eq. 3)

is obtained by causing each term of the above series to correspond to the variation of a quantized unit.

The intermittent line 30 in FIG. 3 corresponds to the intermittent lines 20 and 21 in FIG. 2, while the zigzag line 31 corresponds to the zigzag lines 22 and 23. When the pulse distribution indicated in FIG. 1 exists, these zigzag lines in FIGS. 2 and 3 are presumed to respond promptly to a variation in the quantized unit without a delay in a pluse.

In FIG. 1, the auxiliary variable t is represented by the sum of the series, and the symbols@ indicating the pulse distribution are disposed at the ends of their respective terms.The positions at which the symbols@ l8are disposed may be selected at will within the limits of their respective terms. Furthennore, pulse distribution is not effected when the velue of a term is zero.

A straight line'is generated in a manner as indicated in FIGS. 4 and 5. In the case where linear interpolation 

1. A function generating system comprising, relative to an objective value (X,Y) in a plane, a first register for storing a numerical value X, a second register for storing a numerical value Y smaller than X, a gate for passing the output of the first register when the qualitative value (positive, negative, or zero), for a preceding operational reslut Delta '', is zero or negative, and for blocking the same when said qualitative value is positive, a complement circuit coupled to receive an output signal from the second register, an adder circuit for adding the preceding operational result Delta '' and output signals from said gate and said complement circuit, and a third register having an input coupled to the output of said adder circuit for receiving the present operational result Delta therefrom and including means for storing the quantity Delta and for feeding back its own output as an input to the adder circuit for the succeeding operation, wherein the present value for Delta is determined as (preceeding operational result Delta '')+X-Y( for preceding operational result Delta '' < OR = 0), (preceding operational result Delta '')-Y(for preceding operational result Delta ''>0), where pulse distribution is periodically carried out for the X axis, so that when said present value at Delta < OR = 0, one pulse distribution is effected for the Y axis.
 2. A function generating system according to claim 1 in which the coordinates of the center of a circle are taken as the said objective value, and further comprising means for subtracting one quantized unit from the first register each time a pulse is generated in the axis direction relating to said numerical value X, and for adding one quantized unit to the second register each time a pulse is generated in the axis direction related to said numerical value Y.
 3. A function generating system according to claim 1 in which the coordinates (X,Y) of a point are taken as the objective value, and further comprising means for adding one quantized unit to the first register each time a pulse is generated in the axis direction related to said numerical value X, and for adding one quantized unit to the second register each time a pulse is generated in the axis direction related to said numerical value Y.
 4. A function generating system according to claim 1 in which the coordinates (X,Y) of a point are taken as the objective value, and further comprising means for adding one quantized unit to the second register, and for generating pulses in the axis direction related to said numerical value Y m times per n cycles (where m and n are constants), when the present operational result Delta is zero or negative, each time a pulse is generated in the axis direction related to said numerical value X.
 5. A function generating system according to claim 1 including means for setting a numerical value X+1 in the first register, and a numerical value Y+1 in the second register. 